Teacher Support Materials 2009 Maths GCE Paper Reference MS/SS/1B Copyright © 2009 AQA and its licensors All rights reserved Permission to reproduce all copyrighted material has been applied for In some cases, efforts to contact copyright holders have been unsuccessful and AQA will be happy to rectify any omissions if notified The Assessment and Qualifications Alliance (AQA) is a company limited by guarantee registered in England and Wales (company number 3644723) and a registered charity (registered charity number 1073334) Registered address: AQA, Devas Street, Manchester M15 6EX Dr Michael Cresswell, Director General MS/SS1B Question Student Response Commentary As was usually the case, the candidate has scored full marks in parts (a)(i), (ii) & (iii), 92 although in the latter part an incorrect answer of was regularly seen Part (a)(iv) was 160 often more of a challenge and here the candidate has found P(Paperback | Thriller) The candidate’s answer to part (b) was by far the most common The three correct subject totals have been divided by 160, 159 & 158 respectively (those who used 160 lost a further mark) but no account has been taken of the 3! = permutations Mark scheme MS/SS1B Question Student Response Commentary Whilst many candidates scored full marks for this question, the above solution illustrates some common errors that lost marks Given Instruction on the Front Page of the Question Paper, the value of r was required to at least three decimal places Part (b) required a reference to the strength and the sign of the correlation in context; all referenced here The points are accurately plotted and labelled (candidates were penalised for omitting the latter) The candidate has identified the two most likely female snakes but the estimated value of r for the remaining male snakes is outside the acceptable range of 0.25 to 0.75, actual value is 0.488 Despite a correct revised interpretation, the final mark is not available as it is dependent upon the estimated value of r being within the acceptable range MS/SS1B Mark Scheme Question MS/SS1B Student Response Commentary The normal distribution sketches have enabled the candidate to identify the appropriate areas (< 0.5 or > 0.5) and only an arithmetic slip has prevented full marks in part (a)(ii) Many candidates gave an answer of 0.72575 to part (a)(i) and one of o.67095 to part (a)(ii) Such answers only scored a total of or marks About 50% of candidates attempted calculations in part (a)(iii) for no reward whatsoever The above answer to part (b) shows the two most common errors; an incorrect z-value coupled with the mysterious loss of a negative sign! Mark Scheme MS/SS1B Question Student Response Commentary Undoubtedly, the best answered question on the paper with a mode of marks The above illustrates a typical concise solution A correct equation (to appropriate accuracy – not –0.55) followed by the (rather unnecessary) substitution of x = with an answer as requested to the nearest gram In part (c), the candidate has shown the necessary substitution of 91 to give y followed by a sensible conclusion At this final step, a minority of candidates felt that any (minute) weight disproved the claim! Those candidates who substituted y = to give x 91 were equally rewarded However comments only referencing ‘extrapolation’ did not gain full marks Mark Scheme MS/SS1B Question Student Response MS/SS1B Commentary Unlike here, it was not unusual to simply see stated correct answers to parts (a)(i) & (ii) Where such stated answers were incorrect, often or even marks were lost Many candidates, as here, also answered parts (b)(i) & (ii) correctly; some even obtaining 1.69 after making a total mess of part (a)(ii) Almost all answers to part (a)(iii), as here, were incorrect though usually claiming ‘correct’ due to either a large sample or the CLT This revealed a marked lack of knowledge of the latter A large (>30 say) sample enables one to assume that the sample mean is approximately normally distributed; not the sample and certainly not the population! Mark Scheme Question Student Response Commentary Very few candidates scored full marks here; the above illustrates typical mistakes Perhaps as a result of Question 3(b), the candidate has used an incorrect z-value in part (a) and so lost of the marks Part (b) involving standard error is completely correct; illustrating the noticeable improvement Standardising using = 28 lost all marks In answering part (c), the candidate has identified (b) correctly but, in common with almost all candidates, has not given the correct reason that the distribution of Y was unknown MS/SS1B Mark Scheme Question MS/SS1B Student Response Commentary Whilst most candidates scored quite well on this question, few gained full or nearly full marks Marks were often lost in part (a) for quoting 0.8801 as the answer to (i) and/or, as here, using one incorrect value in (ii) Whilst it was very rare indeed to see an incorrect answer to part (b)(i), it was equally rare to see a correct answer to part (b)(ii) The above illustrates a typical error of calculating – P(1) rather than – P(0) In common with this candidate, almost all candidates were able to score full marks in part (b)(iii), though a minority ignored the word ‘correctly’ In order to score any marks in part (b)(iv), a comparison of means and/or variances was required Whilst this candidate has so done for the first mark, subsequent statements are incorrect conclusions Mark Scheme [...]... MS/SS1B Commentary Unlike here, it was not unusual to simply see stated correct answers to parts (a)(i) & (ii) Where such stated answers were incorrect, often 3 or even 6 marks were lost Many candidates, as here, also answered parts (b)(i) & (ii) correctly; some even obtaining 1.69 after making a total mess of part (a)(ii) Almost all answers to part (a)(iii), as here, were incorrect though usually claiming... = 28 lost all 4 marks In answering part (c), the candidate has identified (b) correctly but, in common with almost all candidates, has not given the correct reason that the distribution of Y was unknown MS/SS1B Mark Scheme Question 7 MS/SS1B Student Response Commentary Whilst most candidates scored quite well on this question, few gained full or nearly full marks Marks were often lost in part (a)... part (a) for quoting 0.8801 as the answer to (i) and/or, as here, using one incorrect value in (ii) Whilst it was very rare indeed to see an incorrect answer to part (b)(i), it was equally rare to see a correct answer to part (b)(ii) The above illustrates a typical error of calculating 1 – P(1) rather than 1 – P(0) In common with this candidate, almost all candidates were able to score full marks in part... than 1 – P(0) In common with this candidate, almost all candidates were able to score full marks in part (b)(iii), though a minority ignored the word ‘correctly’ In order to score any marks in part (b)(iv), a comparison of means and/or variances was required Whilst this candidate has so done for the first mark, subsequent statements are incorrect conclusions Mark Scheme ... ‘correct’ due to either a large sample or the CLT This revealed a marked lack of knowledge of the latter A large (>30 say) sample enables one to assume that the sample mean is approximately normally distributed; not the sample and certainly not the population! Mark Scheme Question 6 Student Response Commentary Very few candidates scored full marks here; the above illustrates typical mistakes Perhaps